Surface Area of Composite Solids

Geometric Shape	Surface Area B = area of the base P = perimeter of the base	Volume B = area of the base P = perimeter of the base
prism (general)	SA = 2B + Ph	V = Bh
triangular prism	SA = 2B + Ph SA = 2(1/2ab) + (b + c + d)h SA = ab + (b + c + d)h	V = Bh V = 1/2 abh
rectangular prism	SA = 2B + Ph SA = 2(lw) + (2l + 2w)h	V = lwh
Regular square prism	SA = 2B + Ph SA = 2(s2) + (4s)h	V = Bh V = s2h
regular pentagonal prism	SA = 2B + Ph SA = 2(1/2ans) + nsh SA = 2(1/2a)(5)s + 5sh SA = 5as + 5sh	V = Bh V = 1/2ansh V = 1/2a(5)sh V = 5/2ash
regular hexagonal prism	SA = 2B + Ph SA = 2(1/2ans) + nsh SA = 2(1/2a)(6)s + 6sh SA =6as + 6sh	V = Bh V = 1/2ansh V = 1/2a(6)sh V = 3ash
cube	SA = 2B + Ph SA = 2(s2) + (4s)s = 6s2	V = Bh V = s3
regular pyramid (general)	SA = B + n(1/2sl) l = slant height	V = 1/3Bh
regular triangular pyramid	SA = B + n(1/2sl) SA = 1/2as + (3)(1/2sl) SA = 1/2as + 3/2sl l = slant height	V = 1/3Bh V = 1/3(1/2 ab)h V = 1/6 abh
regular square pyramid	SA = B + n(1/2sl) SA = s2 + (4)(1/2sl) SA = s2 + 2sl l = slant height	V = 1/3Bh V = 1/3(b2)h = 1/3b2h
regular pentagonal pyramid	SA = B + n(1/2sl) SA = 1/2a(5)s + (5)(1/2sl) SA = 5/2as + 5/2sl l = slant height	V = 1/3Bh V = 1/3(1/2anb)h V = 1/6 anbh
regular hexagonal pyramid	SA = B + n(1/2sl) SA = 1/2a(6)s + (6)(1/2sl) SA = 3as + 3sl l = slant height	V = 1/3Bh V = 1/3(1/2anb)h V = 1/6 anbh
cylinder	SA = 2B + ph SA = 2(p r2) + (2pr)h	V = Bh V = p r2h

Some suggestions of your project work's answers

PART I:

Get the information from internet, related it to the mathematics field such as Geometry, Progressions, Calculus, and so on.

PART II:

1) To find the diameter of baking tray to be used to fit the 5 kg cake (1 kg = 3800 cm^3), all you need is the formula of volume of cylinder, V = pi x (d/2)^2 x h. You should get the answer 58.78 cm.

2) (a) To find the corresponding values of diameters of the baking tray to be used, all you need is the formula that related h and d, which is the formula of volume of cylinder, V = pi x (d/2)^2 x h, and you are given that the weight of the cake must be 5kg, so you should able to find it's volume since 1 kg = 3800 cm^3.

(b) (i) To find the range of heights that is NOT suitable for the cakes, you just have to think logically, the height and the diameter of the cake should not exceed the inner dimensions of the oven.

(ii) The answer is not fixed, you just have to explain why you choose that dimension.

(c) This question is related to Linear Law, since the question asks you to form an equation to represent the LINEAR relation between h and d. You must form the linear equation by reducing the equation V = pi x (d/2)^2 x h, where the V already given, in cm^3. Your Y and X must consist of h and/or d, and your m and c only consist of constant, but not h and/or d. After that plot your line of best fit.

(ii) (a)  Just refer to your line of best fit to find the diameter of the round cake pan required where height of the cake is 10.5. Just do as what normally we do, just don't forget that the value you get from the line of best fir is either Y/X!! You have to calculate again to get your d!


(ii) (b) Same as (ii) (a), the only different is you need to find h by referring to the d = 42 cm

3) (a) By referring to your 2(b)(ii), you can estimate the amount of fresh cream just by using the formula of total surface, A = pi x r^2 + 2 x pi x r x h. The original formula of total surface area of a cylinder should be A = 2 x pi x r^2 + 2 x pi x r x h, but please think logically, we are not going to put any cream at the BOTTOM of the cake, so we we only need to consider the top surface area of the cake.You should able to find the amount (volume, in cm^3) of fresh cream required to decorate the cake, where the thickness of the cream is 1 cm.

(b) Suggest three other shapes for cake besides cylinder. You may refer to the shapes such as cube, cuboid, triangular prism, pentagon-shape based solid, and so on. Different shape will have different way to find the total surface area. You should able to find the amount (volume, in cm^3) of fresh cream required to decorate the cake, where the thickness of the cream is 1 cm.

(c) By referring to the volume of cream required for the cylinder cake and the other three different shapes of cake suggested in (b), determine the shape requires the least amount of fresh cream to be used.

PART III:

The method that you may refer are differentiation (Calculus) and Completing the Square from Quadratic Functions. The question asks for the dimension of a 5 kg round cake that requires the minimum amount of fresh cream, from here you should know (i) minimum total surface area will requires minimum amount of fresh cream, (ii) the weight of the cake already fixed at 5 kg, this means the volume of cake also fixed (1kg = 3800 cm^3), (iii) The height, h and the diameter, d of the cake will give you the dimension of the cake, so you need to derive an equation of total surface area (not involved the bottom of the cake) in terms of h or d/r (r = d/2), so that later on you can find the values of them.

Volume, V =pi x r^2 x h

Total surface area (not include bottom of cake), A = pi x r^2 + 2 x pi x r x h

Differentiation:

You may get the equation of A in terms of h or d/r here (better A in terms of d/r, and you should able to get A = pi/4 x d^2 + 76000/d  or  A = pi x r^2 + 38000/r if you refer to radius, r).
If referring to A = pi x r^2 + 38000/r, dA/dr = 0 when total surface area is minimum, from here you should able to get the values of r, and then the corresponding values of d (d = 2r).

Completing the Square:

If referring to A = pi x r^2 + 2 x pi x r x h, factorize the pi so that a = 1, you will get A = pi (r^2 + 2hr), then do the completing the square to find the r in terms of h, after that substitute it inside V =pi x r^2 x h to get the value of h and r (negative value will be rejected, impossible).

After this, determine whether you want to bake the cake with this dimension or not, explain your decision.

FURTHER EXPLORATION:

(a) This question is related to progression, because the radius of the next cake will be 10% less than the previous cake, determine whether this is AP or GP, and then determine the a and d/r so that you can find the volume of the first, second, third and fourth cakes.

(b) Total mass of all cakes (Sn) not exceed (<) 15 kg, Sn < 15, and you need the formula of sum of terms. After you get the answer, verify your answer by other methods, you may use the listing method, list down one by one.

REFLECTION:

Based on your own creativity.

CONCLUSION:

Briefly conclude everything that you have done in this project.

Ganbate!!!

Bibliography with APA (American Psychological Association) format: Electronic Sources (Web Publications)

Article From an Online Periodical

Online articles follow the same guidelines for printed articles. Include all information the online host makes available, including an issue number in parentheses.

Author, A. A., & Author, B. B. (Date of publication). Title of article.Title of Online Periodical, volume number(issue number if available). Retrieved from http://www.someaddress.com/full/url/

Bernstein, M. (2002). 10 tips on writing the living Web. A list apart: For people who make websites, 149. Retrieved from http://www.alistapart.com/articles/writeliving

Newspaper Article

Author, A. A. (Year, Month Day). Title of article. Title of Newspaper. Retrieved from http://www.someaddress.com/full/url/

Parker-Pope, T. (2008, May 6). Psychiatry handbook linked to drug industry. The New York Times. Retrieved from http://www.nytimes.com

Electronic Books

Electronic books may include books found on personal websites, databases, or even in audio form. Use the following format if the book you are using is only provided in a digital format or is difficult to find in print. If the work is not directly available online or must be purchased, use "Available from," rather than "Retrieved from," and point readers to where they can find it. For books available in print form and electronic form, include the publish date in parentheses after the author's name.

De Huff, E. W. (n.d.). Taytay’s tales: Traditional Pueblo Indian tales. Retrieved from http://digital.library.upenn.edu/women/dehuff/taytay/
taytay.html

Davis, J. (n.d.). Familiar birdsongs of the Northwest. Available from http://www.powells.com/cgi-bin/biblio?inkey=1-
9780931686108-0

Chapter/Section of a Web document or Online Book Chapter

Author, A. A., & Author, B. B. (Date of publication). Title of article. In Title of book or larger document (chapter or section number). Retrieved from http://www.someaddress.com/full/url/

Engelshcall, R. S. (1997). Module mod_rewrite: URL Rewriting Engine. InApache HTTP Server Version 1.3 Documentation (Apache modules). Retrieved from http://httpd.apache.org/docs/1.3/mod/mod_rewrite.html

Peckinpaugh, J. (2003). Change in the Nineties. In J. S. Bough and G. B. DuBois (Eds.), A century of growth in America. Retrieved from GoldStar database.

NOTE: Use a chapter or section identifier and provide a URL that links directly to the chapter section, not the home page of the Web site.

Online Encyclopedias and Dictionaries

Often encyclopedias and dictionaries do not provide bylines (authors' names). When no byline is present, move the entry name to the front of the citation. Provide publication dates if present or specify (n.d.) if no date is present in the entry.

Feminism. (n.d.). In Encyclopædia Britannica online. Retrieved from http://www.britannica.com/EBchecked/topic/724633/feminism

Online Lecture Notes and Presentation Slides

When citing online lecture notes, be sure to provide the file format in brackets after the lecture title (e.g. PowerPoint slides, Word document).

Hallam, A. Duality in consumer theory [PDF document]. Retrieved from Lecture Notes Online Web site: http://www.econ.iastate.edu/classes/econ501/Hallam/
index.html

Roberts, K. F. (1998). Federal regulations of chemicals in the environment [PowerPoint slides]. Retrieved from http://siri.uvm.edu/ppt/40hrenv/index.html

Nonperiodical Web Document, Web Page, or Report

List as much of the following information as possible (you sometimes have to hunt around to find the information; don't be lazy. If there is a page like http://www.somesite.com/somepage.htm, and somepage.htm doesn't have the information you're looking for, move up the URL to http://www.somesite.com/):

Author, A. A., & Author, B. B. (Date of publication). Title of document. Retrieved from http://Web address

Angeli, E., Wagner, J., Lawrick, E., Moore, K., Anderson, M., Soderland, L., & Brizee, A. (2010, May 5). General format. Retrieved from http://owl.english.purdue.edu/owl/resource/560/01/

NOTE: When an Internet document is more than one Web page, provide a URL that links to the home page or entry page for the document. Also, if there isn't a date available for the document use (n.d.) for no date.

Online Forum or Discussion Board Posting

Include the title of the message, and the URL of the newsgroup or discussion board. Please note that titles for items in online communities (e.g. blogs, newsgroups, forums) are not italicized. If the author's name is not available, provide the screen name. Place identifiers like post or message numbers, if available, in brackets. If available, provide the URL where the message is archived (e.g. "Message posted to..., archived at...").

Frook, B. D. (1999, July 23). New inventions in the cyberworld of toylandia [Msg 25]. Message posted to http://groups.earthlink.com/forum/messages/00025.html

Blog (Weblog) and Video Blog Post

Include the title of the message and the URL. Please note that titles for items in online communities (e.g. blogs, newsgroups, forums) are not italicized. If the author’s name is not available, provide the screen name.

J Dean. (2008, May 7). When the self emerges: Is that me in the mirror? [Web log comment]. Retrieved from http://www.spring.org.uk/the1sttransport

Psychology Video Blog #3 [Video file]. Retrieved from http://www.youtube.com/watch?v=lqM90eQi5-M

Wikis

Please note that the APA Style Guide to Electronic References warns writers that wikis (like Wikipedia, for example) are collaborative projects that cannot guarantee the verifiability or expertise of their entries.

OLPC Peru/Arahuay. (n.d.). Retrieved April 29, 2011 from the OLPC Wiki: http://wiki.laptop. org/go/OLPC_Peru/Arahuay

Bibliography with APA (American Psychological Association) format: Books

Basic Format for Books

Author, A. A. (Year of publication). Title of work: Capital letter also for subtitle. Location: Publisher.

Note: For "Location," you should always list the city and the state using the two letter postal abbreviation without periods (New York, NY).

Calfee, R. C., & Valencia, R. R. (1991). APA guide to preparing manuscripts for journal publication. Washington, DC: American Psychological Association.

Edited Book, No Author

Duncan, G. J., & Brooks-Gunn, J. (Eds.). (1997). Consequences of growing up poor. New York, NY: Russell Sage Foundation.

Edited Book with an Author or Authors

Plath, S. (2000). The unabridged journals K.V. Kukil, (Ed.). New York, NY: Anchor.

A Translation

Laplace, P. S. (1951). A philosophical essay on probabilities. (F. W. Truscott & F. L. Emory, Trans.). New York, NY: Dover. (Original work published 1814).

Note: When you cite a republished work, like the one above, in your text, it should appear with both dates: Laplace (1814/1951).

Edition Other Than the First

Helfer, M. E., Kempe, R. S., & Krugman, R. D. (1997). The battered child (5th ed.). Chicago, IL: University of Chicago Press.

Article or Chapter in an Edited Book

Author, A. A., & Author, B. B. (Year of publication). Title of chapter. In A. Editor & B. Editor (Eds.), Title of book (pages of chapter). Location: Publisher.

Note: When you list the pages of the chapter or essay in parentheses after the book title, use "pp." before the numbers: (pp. 1-21). This abbreviation, however, does not appear before the page numbers in periodical references, except for newspapers.

O'Neil, J. M., & Egan, J. (1992). Men's and women's gender role journeys: Metaphor for healing, transition, and transformation. In B. R. Wainrib (Ed.), Gender issues across the life cycle (pp. 107-123). New York, NY: Springer.

Multivolume Work

Wiener, P. (Ed.). (1973). Dictionary of the history of ideas (Vols. 1-4). New York, NY: Scribner's.

Bibliography with APA (American Psychological Association) format: Author/Authors

Single Author

Last name first, followed by author initials.

Berndt, T. J. (2002). Friendship quality and social development.Current Directions in Psychological Science, 11, 7-10.

Two Authors

List by their last names and initials. Use the ampersand instead of "and."

Wegener, D. T., & Petty, R. E. (1994). Mood management across affective states: The hedonic contingency hypothesis. Journal of Personality & Social Psychology, 66, 1034-1048.

Three to Seven Authors

List by last names and initials; commas separate author names, while the last author name is preceded again by ampersand.

Kernis, M. H., Cornell, D. P., Sun, C. R., Berry, A., Harlow, T., & Bach, J. S. (1993). There's more to self-esteem than whether it is high or low: The importance of stability of self-esteem. Journal of Personality and Social Psychology, 65, 1190-1204.

More Than Seven Authors

Miller, F. H., Choi, M. J., Angeli, L. L., Harland, A. A., Stamos, J. A., Thomas, S. T., . . . Rubin, L. H. (2009). Web site usability for the blind and low-vision user. Technical Communication, 57, 323-335.

Organization as Author

American Psychological Association. (2003).

Unknown Author

Merriam-Webster's collegiate dictionary (10th ed.).(1993). Springfield, MA: Merriam-Webster.

NOTE: When your essay includes parenthetical citations of sources with no author named, use a shortened version of the source's title instead of an author's name. Use quotation marks and italics as appropriate. For example, parenthetical citations of the source above would appear as follows: (Merriam-Webster's, 1993).

Two or More Works by the Same Author

Use the author's name for all entries and list the entries by the year (earliest comes first).

Berndt, T. J. (1981).

Berndt, T. J. (1999).

When an author appears both as a sole author and, in another citation, as the first author of a group, list the one-author entries first.

Berndt, T. J. (1999). Friends' influence on students' adjustment to school. Educational Psychologist, 34, 15-28.

Berndt, T. J., & Keefe, K. (1995). Friends' influence on adolescents' adjustment to school. Child Development, 66, 1312-1329.

References that have the same first author and different second and/or third authors are arranged alphabetically by the last name of the second author, or the last name of the third if the first and second authors are the same.

Wegener, D. T., Kerr, N. L., Fleming, M. A., & Petty, R. E. (2000). Flexible corrections of juror judgments: Implications for jury instructions. Psychology, Public Policy, & Law, 6, 629-654.

Wegener, D. T., Petty, R. E., & Klein, D. J. (1994). Effects of mood on high elaboration attitude change: The mediating role of likelihood judgments. European Journal of Social Psychology, 24, 25-43.

Two or More Works by the Same Author in the Same Year

If you are using more than one reference by the same author (or the same group of authors listed in the same order) published in the same year, organize them in the reference list alphabetically by the title of the article or chapter. Then assign letter suffixes to the year. Refer to these sources in your essay as they appear in your reference list, e.g.: "Berdnt (1981a) makes similar claims..."

Berndt, T. J. (1981a). Age changes and changes over time in prosocial intentions and behavior between friends. Developmental Psychology, 17, 408-416.

Berndt, T. J. (1981b). Effects of friendship on prosocial intentions and behavior. Child Development, 52, 636-643.

Introductions, Prefaces, Forewords, and Afterwords

Cite the publishing information about a book as usual, but cite Introduction, Preface, Foreword, or Afterword (whatever title is applicable) as the chapter of the book.

Funk, R. & Kolln, M. (1998). Introduction. In E.W. Ludlow (Ed.),Understanding English Grammar (pp. 1-2). Needham, MA: Allyn and Bacon.

Mathtype

Please download the Mathtype so that you can type the mathematics equations easily.

For those who cannot unzip the rar file, please download the winRAR

Information about Additional Mathematics Project Work 2011

This is the Additional Mathematics Project Work question 2 - Wedding Cake:
BI version
BM version

This is the Guideline, please refer the objectives here.

This is the Rubrics Project Work 2011, the criteria of giving score, please take a look on what criteria you must have in your project work.

You are given 3 weeks to complete the project work 2011, I will start counting from 1 Jun 2011.